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Question

If the length of each edge of a cube is doubled, how many times does its volume become? How many times does its surface area become?

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Solution

Let a be the length of the edge of a cube.
Volume of the cube=a3
Total surface area=6a2

If the length is doubled, then the new length becomes 2a.
Now, new volume =(2a)3=8a3
Also, new surface area==6(2a)2=6×4a2=24a2
∴ The volume is increased by a factor of 8, while the surface area increases by a factor of 4.

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